There are several equivalent forms of these on-shell Dirac-spinors' projectors
in 4 dimensions. In particular, one may commute the on-shell projection
operator \({p} \pm m\)  and the polarization projection operator
\(({1+\gamma _5 {S}_p})/{2}\)  using \(p \cdot S_p = 0\) .
However, it is well known that a fully anticommuting \(\gamma _5\)  can not be
implemented in dimensional regularization in an algebraically consistent way [1]},
if we still want this object to coincide with the usual \(\gamma _5\)  in 4 dimensions.
In this article, we adopt the \(\gamma _5\)  prescription of ref. [2]}, [3]},
conventionally known as Larin's scheme, whose equivalent but more efficient implementations in high-order
perturbative calculations are discussed in ref. [4]}.
In our work, all appearances of \(\gamma _5\)  matrices, originating either from
interaction vertices or external polarization projectors, should be
regarded just for bookkeeping purposes and their interpretations shall be based
on [2]}, [3]}, [4]}.
As a consequence of this prescription, \(\gamma _5\)  no longer anticommutes with all
Dirac \(\gamma \)  matrices, and 4-dimensional equivalent forms of eq. (REF )
are no longer necessarily algebraically equivalent in D dimensions.
